We mention that \(|\mathcal {H}| > k+2\)  comes without loss of generality.The constraint \(|\mathcal {H}| > k+2\)  rules out some degenerate scenarios, we kindly refer to appendix:cardinality of H.
In contrast to the standard PAC model, any concept class is learnable in the universal rates setting [1]}. Intuitively, the analogue of non-learnability in the uniform setting is the case of arbitrarily slow rates.
Our second result is the specification of some combinatorial complexity measures of \(\mathcal {H}\)  that characterize the optimal learning rate of this class. Let us first provide some informal definitions of these measures. We begin with the notion of multiclass Littlestone trees, which extends the binary Littlestone trees from [2]}.
